Prison Escape - Solving Prisoner’s Dilemma with Machine Learning

Demystifying the Most Famous Game Theory Problem

In today’s article, we are going to demystify the most famous Game Theory problem - Prisoner’s Dilemma. We are going to study the problem itself, as well as the strategies that can be used to approach it. Ultimately we are going to conduct a tournament to find the most successful strategy. By the end of this article, you will be familiar with the Prisoner’s Dilemma mechanics and its implications that can be useful in many real-world situations.

Prisoner’s Dilemma (PD)

Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge, but they have enough to convict both on a lesser charge. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent. The offer is:

If A and B each betray the other, each of them serves 2 years in prison

If A betrays B but B remains silent, A will be set free and B will serve 3 years in prison (and vice versa)

If A and B both remain silent, both of them will only serve 1 year in prison.

Above payoff matrix is crucial to understand the underlying mechanics of the problem. While we can clearly see that there is no one-size-fits-all solution, can we come up with a strategy that will maximize our rewards?

Although prisoner’s interrogation is a good and descriptive example, it’s just one of the many possible scenarios that can fit the PD game model. Before we dive deeper into PD, let’s move on to the real-life examples to find out what may be the other possibilities of this game theory problem.